Arising from an effort to design a compact magnetron that would produce approximately 1 GW output power at or near a frequency of 1.3 GHz, it was determined that the traditional radial extractor design would not fit into the desired size constraints, as shown in FIG. 1. Thus there developed a need to design a new way for extracting microwave power from a magnetron while maintaining a compact, efficient package.
The new axial extractor design was derived from considering the magnetic coupling employed by a rectangular slotted waveguide antenna and applying reciprocity. A piece of a typical slotted waveguide antenna, designed to radiate the lowest order (TE10) mode, is shown in FIG. 2. Note that, in order to radiate, the slots must be placed such that the current on the waveguide wall is interrupted. For a TE10 mode propagating in a hollow waveguide, the time harmonic electromagnetic fields in phasor form (e−iωt time convention) are given by
      E    =                  y        ^            ⁢              E        0            ⁢              sin        (                              π            a                    ⁢          x                )            ⁢              ⅇ                              ⅈk            z                    ⁢          z                          H    =                                        E            0                                η            0                          ⁡                  [                                                    -                                  x                  ^                                            ⁢                                                k                  z                                k                            ⁢                              sin                (                                                      π                    a                                    ⁢                  x                                )                                      -                                          zi                ^                            ⁢                              π                ka                            ⁢                              cos                (                                                      π                    a                                    ⁢                  x                                )                                              ]                    ⁢              ⅇ                              ⅈk            z                    ⁢          z                    where E0 is the wave amplitude, η0 is the impedance of the free space, k=w/c=2π/λ0 is the free space electromagnetic wavenumber, ω is the radian frequency, c is the speed of light, kz=√{square root over (k2−(π/a)2)}=2π/λg is the waveguide propagation constant, λ0 is the free space electromagnetic wavelength, λg is the wavelength inside the waveguide, and i=√{square root over (−1)}. The surface current density in the top waveguide wall is then given by
      J    s    =                    -                  y          ^                    ×      H        =                                        E            0                                η            0                          ⁡                  [                                                    xi                ^                            ⁢                              π                ka                            ⁢                              cos                (                                                      π                    a                                    ⁢                  x                                )                                      -                                          z                ^                            ⁢                                                k                  z                                k                            ⁢                              sin                (                                                      π                    a                                    ⁢                  x                                )                                              ]                    ⁢              ⅇ                              ⅈk            z                    ⁢          z                    
Thus, the transverse ({circumflex over (x)}-directed) current on the top wall has a cosine distribution with a null along the center axis of the wall. A slot cut along the center axis of the wall does not radiate, which is the reason the slots in FIG. 2 are located off the center axis. Further, the radiation from two side-by-side slots symmetric about the center axis of the wall is 180° out of phase and tends to cancel. Thus, the slots on the opposite sides of the center axis of the wall are spaced one half of a waveguide wavelength (λg/2) so the radiation is in phase. By reciprocity, to excite a TE10 mode in a rectangular waveguide through a slot in a broad wall, the slot must be located off the center axis of the wall. Two side-by-side slots on opposite sides of the center axis excite the TE10 mode if they are driven 180° out of phase.
Based on the slotted waveguide antenna and reciprocity, coupling slots to a rectangular waveguide are cut in the end walls of alternating cavities of the magnetron. Each waveguide axis is aligned with the magnetron axis, as shown in FIGS. 3a and 3b. The development of this magnetic coupling scheme with rectangular, axially-orientated extraction waveguides did not resolve the compactness requirements, but was a vital stepping stone to the development of the all cavity magnetron axial extractor.